With the centerline Mach-number distributions provided in advance, a two-dimensional supersonic wave-cancelled channel was designed by the Method of Characteristics. The shock train，wall static pressure distributions and separation region were investigated. The relationship between the shock train and back pressure was also investigated. The flow-field had dual solutions when the head of the shock train was in the vicinity of the channel inflection. When the flow evolved into the single-solution domain from the dual-solution domain，the larger separated zone transferred quickly and the shock-train structure evolved fast.